Garden City Schools USD #457

Eureka Math ~ 8th Grade Math Curriculum Guide

2020-2021

Math Framework and Protocol

Eureka Math Modifications

Customized District Assessments

Pacing and Assessment Guides

Problem Solving Tasks

Updated May 2018

Garden City Public Schools Garden City, Kansas

Updated May 2018

Mathematics Framework

Garden City Public Schools Statement of Purpose:

To support mathematical proficiency and to meet the challenges of preparing students for College and Career, Garden City Public Schools has developed the following mathematics framework. It provides a synthesis of research-based principles and strategies proven effective in promoting all students’ mathematics development—including the critical, creative, and self-regulated thinking processes that underlie the Kansas College and Career Ready Standards (KCCRS). The KCCRS calls for a shift to focus on sense-making, reasoning, and connections to real-world situations. Students will need knowledge and skills that prepare them to apply mathematics in a variety of contexts, including their future lives as responsible citizens. A transformation is required that results in a greater emphasis on the many ways that math helps us understand the world, and less on math for its own sake. There needs to be a focus on understanding and concepts, not just computation or procedures. Developing and applying real-world situations requires new technology tools and new approaches to teaching and learning. It also requires new assessment methods. The goal of the assessments should be to inform students and teachers about the level of understanding achieved, and of the next necessary steps in instruction. Ongoing informal assessment that guides teaching and learning brings about increased learning as well as increased self-esteem for students. Students will need the resources to prepare them for our rapidly changing world. By working on authentic tasks and real-life problem situations, students make connections related to their own learning of mathematics as well as important new connections among graphic, symbolic, and dynamic representations that are critical in order to understand mathematics effectively. They will also need to recognize that studying mathematics in high school is important for their future careers. A commitment to teacher professional development is essential that is collaborative with time allotted for vertical discussions and alignment across grade levels and high school courses. Teachers will need long-term professional development and support, including opportunities for reflection on their practice and guidance in improving it. To achieve the vision of reasoning and sense-making as the focus of students’ mathematical experiences, all components of the educational system – curriculum, instruction, and assessment – must work together and be designed to support students’ achieving these concepts and skills. Through a coherent and cohesive mathematics program with a strong alignment of curriculum, instruction and assessment, students will have the opportunity to be fully prepared for College and Career challenges.

Updated May 2018

A Vision for School Mathematics (National Council of Teachers of Mathematics NCTM)

Imagine a classroom, a school, or a school district where all students have

access to high-quality, engaging mathematics instruction. There are ambitious expectations for all, with accommodation for those who need it.

Knowledgeable teachers have adequate resources to support their work and are continually growing as professionals. The curriculum is mathematically

rich, offering students opportunities to learn important mathematical concepts and procedures with understanding. Technology is an essential component of the environment. Students confidently engage in complex

mathematical tasks chosen carefully by teachers. They draw on knowledge from a wide variety of mathematical topics, sometimes approaching the

same problem from different mathematical perspectives or representing the mathematics in different ways until they find methods that enable them to

make progress. Teachers help students make, refine, and explore conjectures on the basis of evidence and use a variety of reasoning and proof techniques

to confirm or disprove those conjectures. Students are flexible and resourceful problem solvers. Alone or in groups and with access to

technology, they work productively and reflectively, with the skilled guidance of their teachers. Orally and in writing, students communicate their ideas and results effectively. They value mathematics and engage

actively in learning it.

Updated May 2018

Effective Mathematics Teaching and Learning

An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically. (Principles to Action, NCTM)

Updated May 2018

Standards of Mathematical Practice The Common Core mathematical practice standards are the foundation for mathematical thinking and practice for students as well as guidance that helps teachers modify their classrooms to approach teaching in a way that develops a more advanced mathematical understanding. Think of these standards as a guide to creating a more complex and absorbing learning experience that can be applied to everyday life, instead of being left in the classroom.

1. Make sense of problems and persevere in solving them. The first Common Core mathematical practice standard is found in almost every math problem across the board. It means that students must understand the problem, figure out how to solve it, and then work until it is finished. Common Core standards encourage students to work with their current knowledge bank and apply the skills they already have while evaluating themselves in problem-solving. This standard is easily tested using problems with a tougher skill level than already mastered. While students work through more difficult problems, they focus on the process of solving the problem instead of just getting to the correct answer.

2. Reason abstractly and quantitatively When trying to problem solve, it is important that students understand there are multiple ways to break apart the problem in order to find the solution. Using symbols, pictures or other representations to describe the different sections of the problem will allow students to use context skills rather than standard algorithms.

3. Construct viable arguments and critique the reasoning of others This standard is aimed at creating a common mathematical language that can be used to discuss and explain math as well as support or object others’ work. Math vocabulary is easily integrated into daily lesson plans in order for students to be able to communicate effectively. “Talk moves” are important in developing and building communication skills and can include such simple tasks as restating a fellow classmate’s reasoning or even supporting their own reason for agreeing or disagreeing. Prompting students to participate further in class mathematical discussion will help build student communication skills.

4. Model with mathematics Math doesn’t end at the classroom door. Learning to model with mathematics means that students will use math skills to problem-solve real world situations. This can range from organizing different types of data to using math to help understand life connections. Using real world situations to show how math can be used in many different aspects of life helps math to be relevant outside of math class.

Updated May 2018

Standards of Mathematical Practice (pg. 2)

5. Use appropriate tools strategically One of the Common Core’s biggest components is to provide students with the assets they need to navigate the real world. In order for students to learn what tools should be used in problem solving it is important to remember that no one will be guiding students through the real world – telling them which mathematics tool to use. By leaving the problem open ended, students can select which math tools to use and discuss what worked and what didn’t.

6. Attend to precision Math, like other subjects, involves precision and exact answers. When speaking and problem-solving in math, exactness and attention to detail is important because a misstep or inaccurate answer in math can be translated to affect greater problem-solving in the real world. The importance in this step comes in the speaking demeanor of students to explain what is understood and what isn’t.

7. Look for and make use of structure When students can identify different strategies for problem solving, they can use many different skills to determine the answer. Identifying similar patterns in mathematics can be used to solve problems that are out of their learning comfort zone. Repeated reasoning helps bring structure to more complex problems that might be able to be solved using multiple tools when the problem is broken apart into separate parts.

8. Look for and express regularity in repeated reasoning In mathematics, it is easy to forget the big picture while working on the details of the problem. In order for students to understand how a problem can be applied to other problems, they should work on applying their mathematical reasoning to various situations and problems. If a student can solve one problem the way it was taught, it is important that they also can relay that problem-solving technique to other problems.

Updated May 2018

Identifying High-Quality Mathematics Tasks or Supplemental Resources

The following tool identifies characteristics that are consistently found in high quality tasks. The following rating or review tool should be used to help identify if a mathematical task or supplemental resource is of high quality. It is important to keep in mind that there is no perfect task. Every task can be improved. The tool can be applied to print resources as well as online resources.

Identifying High-Quality Tasks The purpose of the task is to teach or assess:

Conceptual

Understanding

Procedural skill and

fluency

Application

Rating Scale:

2 - Fully Meets the Characteristic

1 - Partially Meets the Characteristic

0 - Does Not Meet the Characteristic

The mathematics task

Rating

Aligns to mathematics content standards I am teaching.

Encourages my students to use representations.

Provides my students with an opportunity for communicating their reasoning.

Has multiple entry points.

Allows for different strategies for finding solutions.

Makes connections between mathematical concepts, between concepts and procedures, or between concepts, procedures, and application.

Prompts cognitive effort.

Is problem-based, authentic, or interesting.

(Retrieved from Mine the Gap for Mathematical Understanding By: John SanGiovanni 2017)

Updated May 2018

Identifying High-Quality Mathematics Tasks or Supplemental Resources (pg. 2)

(Retrieved from Mine the Gap for Mathematical Understanding By: John SanGiovanni 2017)

Updated May 2018

Identifying High-Quality Mathematics Tasks or Supplemental Resources (pg. 3)

(Retrieved from Mine the Gap for Mathematical Understanding By: John SanGiovanni 2017)

Updated May 2018

USD #457 Mathematics Framework

Instructional Components of Eureka Math

• Fluency Practice: (whole group)

• promotes automaticity

• students are engaged

• high paced and energetic

• Application Problem: (whole group)

• independent and/or collaborative

• Kagan structures utilized

• student discourse present-discovers, recognizes, and verbalizes connections

• students understand and utilize RDW

• evidence of movement from concrete to representational to abstract

• students are given the opportunity to solve the problem without teacher guidance

Debrief

Application Fluency

Concept Development

Updated May 2018

USD #457 Mathematics Framework (pg. 2)

• Concept Development(6+ Classwork): (whole group)

• evidence of movement from concrete to representational to abstract (CRA)

• appropriate time is given to establish new learning

• teacher checks for understanding and provides immediate feedback

• student engagement structures may be used (ex: Kagan)

• student discourse present

• Problem Set is utilized in the concept development or as a result of the concept

development

• Debrief (6+ Closing): (whole group)

• PINNACLE of the lesson, if you are short on time, PROTECT THE DEBRIEF

• students articulate the focus of the lesson (metacognition)

• students identify connections between parts of the lesson and/or previous taught concepts

• teachers use rigorous questions to engage students in mathematical dialogue

• Exit Ticket (Independent)

• students are accountable for the day’s learning

• teacher uses tickets to inform instruction

• Homework (Independent)

• reinforces already taught concepts

• builds student confidence

• checks for understanding and confirms independent proficiency

• Centers (optional) (small group/independent)

• centers can be utilized after the completion of all lesson components

• a balance must be present between conceptual vs procedural activities (Suggested 50/50

balance)

• aligned to KCCRS and Eureka Math curriculum

• can be a review of skills already taught in current or previous grade levels

Updated May 2018

USD #457 Mathematics Resource Protocol

Grade Levels Core Resources Approved Supplemental Resources

Intervention Programs

(Tier 2 and 3) Elementary (K-5th)

Eureka Math https://greatminds.org

Problem Solving: • Youcubed https://www.youcubed.org/ • Inside Mathematics www.insidemathematics.org • 3-Act Math Tasks K-6 https://gfletchy.com/3-act-

lessons/ • Nrich Enriching Mathematics https://nrich.maths.org • Problem Solving In All Seasons By: Kim Markworth, Jenni

McCool, & Jennifer Kosiak • Federal Way Public Schools Problem Solving Activities

(Activities Aligned to Eureka Math Modules) https://www.fwps.org/page/2060

• Estimation 180 www.estimation180.com • Scholastic Math magazine • Mathematics Georgia Standards of

Excellence www.georgiastandards.org • Robert Kaplinsky Problem Based

Lessons https://robertkaplinsky.com/lessons/ Fluency Support: • Math Fact Strategies Books (Digital Resource book) • Building Conceptual Understanding and Fluency Through

Games – North Carolina (Digital Resource book) • Greg Tang Math www.gregtangmath.com • Mastering Basic Facts Add/Subtraction and

Multiplication/Division By: John San Giovanni • Well Played By: Linda Dacey, Karen Gartland, & Jayne

Bamford Lynch • Elementary Number Talks (Online

Resources) https://elementarynumbertalks.wordpress.com/

Content Support: • Illustrative

Mathematics https://www.illustrativemathematics.org/ • Illuminations http://illuminations.nctm.org/ • K-5 Math Teaching Resources www.k-

5mathteachingresources.com • Mine the Gap for Mathematical Understanding By: John

SanGiovanni • Zearn https://www.zearn.org • Eureka Math Bay Area Regional

Consortium https://embarc.online/ • KSDE Top Math Website

Resources http://community.ksde.org/Default.aspx?tabid=6173

• Mathematics Georgia Standards of Excellence www.georgiastandards.org

Do the Math Number Worlds DreamBox iStation Math Eureka Math (pre-teaching, re-teaching) Zearn http://www.zearn.org ECAM diagnostic assessment and resources (K-2) Number Readiness diagnostic assessment (1st-5th) and resources Mathematics Georgia Standards of Excellence www.georgiastandards.org

Updated May 2018

USD #457 Mathematics Resource Protocol (pg.2)

Middle (6th-8th)

Eureka Math https://greatminds.org

Problem Solving: • Youcubed https://www.youcubed.org/ • Inside Mathematics www.insidemathematics.org • 3-Act Math Tasks 6-

HS: https://docs.google.com/spreadsheets/d/1jXSt_CoDzyDFeJimZxnhgwOVsWkTQEsfqouLWNNC6Z4/edit#gid=0

• 3-Act Math Tasks K-6 https://gfletchy.com/3-act-lessons/

• Nrich Enriching Mathematics https://nrich.maths.org • Estimation 180 www.estimation180.com • Robert Kaplinsky Problem Based

Lessons https://robertkaplinsky.com/lessons/ Fluency Support: • Math Fact Strategies Books (Digital Resource book) • Building Conceptual Understanding and Fluency Through

Games – North Carolina (Digital Resource book) • Greg Tang Math www.gregtangmath.com • Mastering Basic Facts Add/Subtraction and

Multiplication/Division By: John San Giovanni • Well Played By: Linda Dacey, Karen Gartland, & Jayne

Bamford Lynch Content Support: • Illustrative

Mathematics https://www.illustrativemathematics.org/ • Illuminations http://illuminations.nctm.org/ • K-5 Math Teaching Resources www.k-

5mathteachingresources.com • Mine the Gap for Mathematical Understanding By: John

SanGiovanni • Zearn https://www.zearn.org • Eureka Math Bay Area Regional

Consortium https://embarc.online/ • KSDE Top Math Website

Resources http://community.ksde.org/Default.aspx?tabid=6173

Do the Math Number Worlds DreamBox iStation Math Eureka Math (pre-teaching, re-teaching) Zearn http://www.zearn.org Number Readiness diagnostic assessment (1st-5th) and resources

High (9th – 12th)

Agile Minds (Algebra I and Intensified Algebra)

Problem Solving: • Youcubed https://www.youcubed.org/ • Inside Mathematics www.insidemathematics.org • 3-Act Math Tasks 6-

HS: https://docs.google.com/spreadsheets/d/1jXSt_CoDzyDFeJimZxnhgwOVsWkTQEsfqouLWNNC6Z4/edit#gid=0

• 3-Act Math Tasks K-6 https://gfletchy.com/3-act-lessons/

• Nrich Enriching Mathematics https://nrich.maths.org • Estimation 180 www.estimation180.com • Robert Kaplinsky Problem Based

Lessons https://robertkaplinsky.com/lessons/

Fluency Support:

Updated May 2018

Content Support:

USD #457 Mathematics Resource Protocol (pg. 3)

Recommended Teacher Resources (K-12) Principles to Action By: NCTM

Putting the Practices into Action By: John SanGiovanni & Susanne O’Connell

Teaching Student-Centered Mathematics (PreK-2), (3-5), and (6-8) (CCSS updated version) By: John Van de Walle

5 Practices for Orchestrating Productive Mathematics Discussion By: Mary K. Stein & Margaret Schwan Smith

Classroom Discussions By: Suzanne Chapin

Number Talks (K-5), and (6-8) By: Sherry Parris

Taking Action: Implementing Effective Mathematics Teaching Practices (K-5), (6-8), and (9-12) By: Various Authors

KATM Mathematics Flipbooks http://community.ksde.org/Default.aspx?tabid=5646

Mathematical Mindsets By: Jo Boaler

Mathematics Learning Progressions http://ime.math.arizona.edu/progressions/

KSDE Math Website http://community.ksde.org/Default.aspx?tabid=5255

Home Support Resources Freckle Education www.Freckle.com

Khan Academy www.Khanacademy.com

Prodigy Math Game www.Prodigy.com

Sumdog www.Sumdog.com

Eureka Math www.greatminds.org

Zearn https://www.zearn.org

Modifications to Eureka Math for 2019-2020

Purpose of Modifications for Eureka Math:

• Provide guidelines that will support teachers. • Create a student focused program that supports students and their achievement. • Improve the program to make it better for students, teachers, and parents. • Create a program that has teacher buy-in where teachers can make it their own. • Make Eureka Math a totally positive curriculum for Garden City. • Maximize effectiveness of curriculum for our students.

Parent Communication

• Parent Newsletters: Parent information letter will be sent home explaining how to access digital newsletters. Parents may request paper copies of the newsletters if needed.

• Teachers, coaches, and administrators will address parent concerns related to Eureka Math when they arise.

• www.greatminds.org (free curriculum access, parent newsletters, roadmaps) • If Eureka Math homework and problem sets are used for homework, they must have correct

classroom examples attached. • Digital Homework Helpers are also available to parents and students for assistance with

homework. Information will be sent home each year on how to access these Digital Homework Helpers.

Pacing

• The district math committee recommends 60-90 minutes of math instruction daily for K-6. • Curriculum Guides are provided that includes pacing suggestions. • Math instruction must occur on a daily basis. • All students should receive core math instruction. Students should not be pulled for

supplemental math instruction, intervention, or special services during whole group instruction, (concept development).

• The pacing guides should be used as a guide. Modules should be taught in order to provide for district-wide systemization and to follow the progressions of the KCCRS. This will allow for teacher collaboration during PLC’s and grade level meetings.

Differentiation and Remediation

• Differentiation and remediation have the same goal, to modify instruction until it meets the needs of all learners.

• Differentiation and remediation should occur throughout the lesson as needed. • Scaffolding is folded into the Eureka Math curriculum in such a way that it is part of its very

DNA. Faithful adherence to the modules is the primary scaffolding tool. • If necessary, teachers may use fewer models and/or stay at the concrete level for longer

periods of time, based on individual student needs.

• Teachers should consider the following, which are contained in strategically placed margin notes/scaffolding boxes within the lessons:

o Multiple means of representation o Multiple means of action and expression o Multiple means of engagement o https://www.engageny.org/sites/default/files/resource/attachments/how_to_impl

ement_a_story_of_units.pdf pg. 14-20 This document contains charts for English Language Learners, Students with Disabilities, Students Performing Above Grade Level and Students Performing Below Grade Level.

o https://www.engageny.org/resource/scaffolding-instruction-english-language-learners-resource-guides-english-language-arts-and This document suggests visual or concrete representations, graphic organizers, Kagan, sentence frames, building background knowledge, teacher modeling, and additional strategies.

o This document also contains lesson plans for specific grade levels with suggestions for differentiated instruction.

• Differentiation and remediation can be done during whole group instruction, small group and/or independent work times.

• If gaps in student knowledge exist, teachers should use material from previous Eureka Math lesson(s) whenever possible. Use the search tab to locate material from modules across grade levels. If necessary, supplemental materials aligned with KCCRS (coherence, focus, rigor, 8 SMPs) and Eureka Math may be used. Students still need to be exposed to grade level content, even if you stay at a concrete level longer. • Achieve the Core Coherence Maps https://achievethecore.org/page/1118/coherence-

map This resource connects grade level standards to foundational standards in previous grades and future standards that students will be exposed to.

• Problems in daily instruction can be modified by changing numbers, names, and/or context to increase real-world relevancy. These changes should not change the overall problem type or the objective of the problem. Adjustments CANNOT be made to the Mid and End Module Assessments.

• Resource links: Greatminds.org Zearn.org – created to go with Eureka Math (Grades K-5) Embarconline.org See USD#457 Math Protocol for additional resources.

Complex reading level and vocabulary

• Vocabulary and Reading Level: Through differentiation practices teachers may restate directions so students can better understand the expectations. Teachers may rewrite problems for relevancy and better understanding with the exception of the Mid and End Module Assessments.

• Use a variety of strategies to reinforce vocabulary; word walls, anchor charts, sentence stems, student journals with vocabulary sections, introduce prior to instruction, make connections to math words, show pictures, use visual models, gestures, positive reinforcement, Kagan strategies, connect to concrete or pictorial, etc. See pg. 16 in A Story of Units.

• Embed vocabulary throughout the lesson and review during debriefing.

Centers

• All components of the Eureka lesson (fluency, application problem, concept development, problem set, and debrief) should be completed prior to students completing centers.

• Center activities should include a balance (approximately 50/50) of conceptual vs. procedural activities.

• All center activities need to be aligned to KCCRS and/or Eureka curriculum. • Center activities should cover concepts and skills that have already been taught in the

current school year or previous grade levels.

Special Education

• Special Education teachers are encouraged to use on grade level modules as much as

possible. Teachers should scaffold lessons to meet individual needs and/or IEP goals. • If necessary, SPED teachers may use fewer models and/or stay at the concrete level for

longer periods of time. Whenever possible, students in resource should be exposed to the grade level curriculum and be present for core instruction. The teacher providing support may pull the student from the core classroom after the concept development has been completed to provide accommodated support for the problem set and/or IEP goals.

• Self-contained SPED teachers should teach Eureka Math with fidelity as much as possible. They may use modules from lower grade levels for their instruction and/or go at a slower pace. Supplemental materials should be aligned with the Eureka Math curriculum unless otherwise stated in the student’s IEP.

• Writers of Eureka Math & MTSS team believe that if students are only instructed at a lower grade level, or pulled from core instruction, it increases achievement gaps and increases holes in student knowledge.

Fluency

• Teachers may adjust or repeat Eureka Math fluency activities and sprints multiple times. • When there are multiple fluency activities in an Eureka Math lesson, teachers may choose

the fluency activity(ies) with Eureka that will best prepare students for the lesson. • Students should be active at this time. • When students are counting, teacher may begin with them, but allow students to continue

on their own. • Sprints should not be graded, just trying for student personal best. • Sprints were created with deliberate patterns and sequencing. ( See quadrant example.) • Teachers should facilitate discussion with students about patterns and sequences found

within the Sprints. • Core fluencies are built into the lessons. These can be used as assessments and be graded.

These are particular to grade levels. The page will have a “CF” at the top of the page. The quadrants will also apply to Core Fluencies. 80% of the first column is considered mastery.

• Celebrate successes and aim to get at least one more on the second attempt. • Additional resources can be utilized to support instruction, but not should not replace all

the Eureka fluency activities.

Homework Guidelines

• When homework is assigned, teachers should use the following guidelines. • Homework should be at the independent level of the students, (80% accuracy). We

suggest teachers utilize homework to reinforce facts, computational fluency, and concepts. Do not send work home that is frustrating to students and parents. When Eureka Math homework is used, they must have correct classroom examples attached.

• Absent Students –Teachers should develop a system for absent students that includes notes, examples, peer coaching, etc. Small group time may be used for helping students who have missed instruction. Teachers may video instruction to be watched by students. Homework can be differentiated; students should not be expected to complete all problem sets or homework for extended absences. Teachers should note the overall objectives and teach the big ideas.

• Another option is to copy the lesson from the Teacher’s Manual to send home. • You may send home Sprints for additional practice, since it is not graded and you are trying

for students’ personal best. • Refer to USD #457 Homework Policy and Recommendations prior to assigning homework.

Assessments

• There are two categories of assessments used in Eureka Math, formative and summative. The Customized Mid-Module assessments should be used as formative and/or summative tests. The Customized End-of-Module assessments will be used as summative assessments. Prior to teaching the module, teachers should preview the assessments to establish focus that will guide instruction.

• Formative Assessments: The goal of formative assessments is to gather feedback that can be used by the instructor and the students to guide improvements in the ongoing teaching and learning context. Exit tickets are not required to be entered as grades, but should be used to drive instruction.

• Teacher Flexibility o Teachers have the flexibility to assess as needed to drive instruction. The

components of each lesson that may be used as formative assessments are teacher observations, debriefing questions, exit tickets, and problem sets.

• Summative Assessments: The goal of a summative assessment is to measure the level of proficiency that has been obtained at the end of an instructional unit. End-of-Module assessments will be used as summative assessments.

Technology

• When students use technology, students should be accountable for the practice. Teachers and students should be able to communicate a desired outcome. Rigor should be evident.

• Technology used to strengthen conceptual understanding, fluency, and skill mastery should support the curriculum, not supplant the curriculum.

• Technology appropriate for use by students during core instruction may include virtual manipulatives and student response activities.

• Teachers can use technology to enhance instruction as long as it is aligned to KCCRS and supports the Eureka Math curriculum.

• Please refer to the District Math Protocol for approved curriculum-aligned websites and resources.

USD #457 Customized Eureka Math Assessments (Grades 6-8) The original Eureka Math Mid and End Modules Assessments have been customized by teacher writers from Garden City Public Schools to include a balance of the higher DOK level 2 and 3 questions from the original assessment and module as well as questions from the Illuminate item bank. The purpose of this customization is to ensure all students are being given access to the challenging high level questions throughout the curriculum, while also accessing the foundational skills students need in place to successfully complete those higher level questions. At the beginning of each customized assessment you will find a reference page identifying the standard each question on the customized assessment addresses as well as the original location of that test item, and if the question is procedural, conceptual, or application. Also identified is whether the item will be computer or human scored. Students will log in and take the assessment on Illuminate. For directions on how to assign the assessment to students see the tutorial video Setting Up an Administration of an Illuminate Assessment at https://youtu.be/cxE_eu-tM8A. To ensure consistency with the administration and grading of these assessments, the following must be followed when giving the assessments.

• Assessments are to be completed independently by students. (Questions may be read aloud to students in lower grade levels as needed.)

• Testing accommodations that students receive on state and other classroom assessments, may be provided to students on the customized district assessments.

• Tests are designed to be completed either in one class period or by breaking the assessment apart based on the curriculum pacing. Test administration should be no more than 60 minutes if being administered in one setting.

• Previewing or giving “practice tests” of the assessments is not allowed. • Review of the assessments may only occur after the assessment has been

administered. • Data entry of student assessment scores are to be entered no later than 2

weeks after the module is finished based on the pacing guide provided. Student original assessment scores should be entered into Illuminate to even if review and corrections are made by the student to ensure valid data.

You can also download the Customized District Assessments directly for your grade level at www.gckschools.com under Curriculum and Instruction Resources, Math, and then USD #457 Custom Eureka Assessments.

Eighth Grade Pacing 2019-2020

Within the development of the pacing guides, it is expected that these will be reasonably flexible depending on the needs of your class. The pacing guide for Eighth Grade has 151 days of instruction including 126 days for core lessons, 22 days for assessment administration and feedback, and 14 days for problem solving tasks. In addition to the 151 days of instruction listed above, there is 14 additional days that can be flexed based on state and district assessments and your students’ needs.

Skills spiral throughout the year and students may not be at mastery by the end of an individual lesson. In fact, many lessons anticipate that students will need more practice in concepts. Therefore, it is recommended that if re-teaching needs to happen, it occurs as a part of the next day’s lesson. By doing this, teachers are able to present concepts in several ways and will not get stuck within the same lesson for multiple days. Module Map for Eighth Grade

Module 2 Module 4 Module 5 Module 6 Module 7 (Part 1) & Module 3

Module 1 Module 7 (Part 2)

Module 8 (GC Created)

24 Core Lessons

23 Core Lessons

17 Core Lessons

12 Core Lessons

10 Core Lessons

6 Core Lessons

16 Core Lessons

8 Core Lessons

2 Days for Problem Solving Tasks

2 Days for Problem Solving Tasks

2 Days for Problem Solving Tasks

2 Days for Problem Solving Tasks

2 Days for Problem Solving Tasks

2 Days for Problem Solving Tasks

2 Days for Problem Solving Tasks

n/a

4 Days for Assessment And Feedback

4 Days for Assessment And Feedback

4 Days for Assessment And Feedback

2 Days for Assessment And Feedback

2 Days for Assessment And Feedback

2 Days for Assessment And Feedback

4 Days for Assessment And Feedback

n/a

Suggested 29 Days

Suggested 30 Days

Suggested 24 Days

Suggested 14 Days

Suggested 14 Days

Suggested 10 Days

Suggested 22 Days

Suggested 8 Days

USD #457 8th Grade Eureka Math Pacing and Assessment Guide 2020-2021

Module # of Curriculum Days (Lessons &

Assessments)

Instruction Date Range

Assessment Testing Window

Data Entry Due Date

2: The Concept of Congruence 29 Sept. 14 – Oct. 29 MM: Sept. 22 – Oct. 2 October 2 EM: Oct. 29 – Nov. 5 November 5

4: Linear Equations 30 Oct. 30 – Dec. 16 MM: Nov. 17 – Dec. 3 December 3 EM: Dec. 16 – Dec. 22 December 22

5: Examples of Functions from Geometry 24 Dec. 17 – Feb. 3

MM: Jan. 11 – Jan. 21 January 21 EM: Feb. 3 – Feb. 10 February 10

6: Linear Functions 14 Feb. 4 – March 1 MM: NONE n/a EM: March 1 – March 8 March 8

7 (Part1) and 3: Introduction to Irrational Numbers Using Geometry and Pythagorean Theorem

14 March 2 – March 23 MM: NONE n/a

EM: March 23 – March 30 March 30

1: Scientific Notation 10 March 24 – April 7 MM: NONE n/a EM: April 7 – April 14 April 14

7: (Part 2) Introduction to Irrational Numbers Using Geometry (Lessons 8-23)

22 April 8 – May 7 MM: April 16 – April 28 April 28

EM: May 7 – May 14 May 14

8: Graphing Calculators (Garden City Addition) 8 May 10 – May 19 NONE n/a

Note: This pacing guide allots one day per lesson in each module and 2 days per assessment (one day for administration and one day for reteaching). Combining lessons may need to occur to adjust for state assessments or other scheduling conflicts.

Suggestions on How to Combine Eureka Math Lessons Effectively

Fluency

• If both lessons include a Sprint activity, choose one to complete.

• Examine the objective of each fluency activity and if several have the same objective or cover the same standard, select one activity to complete.

• Do not remove all fluency activities, as they are intentionally included in each lesson to scaffold past learning or prepare students for future topics.

Application Problem • Application Problems review

skills previously learned. Either application problem will achieve this objective.

• Completing both Application Problems is not necessary.

Concept Development/Instruction • Prepare concept development

parts in advance by taking problems from both lessons.

o Identifying your “must dos”, “could dos” and “should dos” on the Problem Sets first and then choosing the Concept Development problems to complete will ensure that instruction matches what students will be expected to do.

• Remaining parts of the concept development can be used to remediate, or extend in small groups.

• It is not suggested to cut out the conceptual development pieces of any lesson. (Ex: student use of models, manipulatives, etc)

Problem Sets/Homework • Combine parts of both Problem Sets

to match parts taught in the Concept Development.

• Customize problems carefully by choosing the most appropriate problems for students.

• Be mindful to not remove all of the deeper level or more challenging problems.

• Creating homework to match your Problem Set is necessary if assigning homework.

Exit Tickets • Combining the Exit Tickets

from both lessons is an excellent way to formatively assess students’ understanding of the content of both lessons.

Eureka Module Eureka Lesson Topic 2010 C.C.S.S.M. (OLD)

2017 K.C.C.R.S (NEW) Changes Resources

2 CONCEPT OF CONGRUENCENEW STANDARDS (ANGLES)

Gr. 4 Mod.4 Topic B Angle Measurement (Lessons 5-8) 4.MD.5, 4.MD.5a, 4.MD.5b, 4.MD.6 8.G.1, 8.G.1a, 8.G.1b, 8.GStandards moved from 4th gradeGr. 4 Mod.4 Topic C Problem Solving with Addition of Angle Measures (Lessons 9-11) 4.MD.7 8.G.3 Standard moved from 4th grade

Assess Mid-Module AssessmentGr.7 Mod. 6 Topic A Unknown Angles (Lessons 1-4) 7.G.5 8.G.4 Standards moved from 7th gradeGr.7 Mod. 6 Topic B Constructing Triangles (Lessons 5-15) 7.G.2 8.G.6 Standards moved from 7th grade

14 More on the Angles of a Triangle 8.G.5 8.G.5 None15 Informal Proof of the Pythagorean Theorem (Optional) 8.G.6 & 8.G.7 8.G.7 & 8.G.8 None16 Applications of the Pythagorean Theorem (Optional) 8.G.6 & 8.G.7 8.G.7 & 8.G.8 None

4 LINEAR EQUATIONS2 Linear and Non linear expressions in X 8.EE.7 8.EE.7 Wording3 Linear Equations in X 8.EE.7 8.EE.7 Wording4 Solving a Linear Equation 8.EE.7 8.EE.7 Wording5 Writing and Solving Linear Equations 8.EE.7b 8.EE.7b Wording6 Solutions of a Linear Equation 8.EE.7a 8.EE.7a Wording7 Classifications of Linear Equations 8.EE.7 8.EE.7 Wording8 Linear Equations in Disguise 8.EE.7b 8.EE.7b Wording9 An Application of Linear Equations 8.EE.7a 8.EE.7a Wording

10 Critical Look at proportional Relationships 8.EE.5 8.EE.4 None11 Constant Rate 8.EE.5 8.EE.4 None12 Linear Equations in Two Variables 8.EE.5 8.EE.4 None13 Graph of a Linear Equation in Variables 8.EE.5 8.EE.4 None14 Graph of a Linear Equation-Horizontal and Vertical Lines 8.EE.5 8.EE.4 None

Assess Mid Module Assessment15 Slope of a non vertical 8.EE.5 & 8.EE.6 8.EE.4 & 8.EE.5 Wording on 8.EE.A.516 Computation of a slope of a non-vertical line 8.EE.5 & 8.EE.6 8.EE.4 & 8.EE.5 Wording on 8.EE.A.517 Line joining two distinct points of the graph y=mx+b with slope m 8.EE.5 & 8.EE.6 8.EE.4 & 8.EE.5 Wording on 8.EE.A.518 There is only one line passing through a given point with a given slope 8.EE.5 & 8.EE.6 8.EE.4 & 8.EE.5 Wording on 8.EE.A.519 The graph of a linear equation in two variables is a line 8.EE.5 & 8.EE.6 8.EE.4 & 8.EE.5 Wording on 8.EE.A.520 Every line is a graph of a linear equation 8.EE.5 & 8.EE.6 8.EE.4 & 8.EE.5 Wording on 8.EE.A.521 Some Facts about linear equations in two variables 8.EE.5 & 8.EE.6 8.EE.4 & 8.EE.5 Wording on 8.EE.A.522 Constant Rates revisited 8.EE.5 & 8.EE.6 8.EE.4 & 8.EE.5 Wording on 8.EE.A.5

NEW STANDARD Proportional in y=mx and Non-proportional in y=mx+b as a result of vertical translation (3 lessons) 8.EE.6 NEW23 Defining Equation of a line 8.EE.5 & 8.EE.6 8.EE.4 & 8.EE.5 Wording on 8.EE.A.5

Assess End-Module Assessment2 CONCEPT OF CONGRUENCE

NEW STANDARDS (ANGLES)Gr. 4 Mod.4 Topic B Angle Measurement (Lessons 5-8) 4.MD.5, 4.MD.5a, 4.MD.5b, 4.MD.6 8.G.1, 8.G.1a, 8.G.1b, 8.GStandards moved from 4th gradeGr. 4 Mod.4 Topic C Problem Solving with Addition of Angle Measures (Lessons 9-11) 4.MD.7 8.G.3 Standard moved from 4th grade

Assess Mid-Module AssessmentGr.7 Mod. 6 Topic A Unknown Angles (Lessons 1-4) 7.G.5 8.G.4 Standards moved from 7th gradeGr.7 Mod. 6 Topic B Constructing Triangles (Lessons 5-15) 7.G.2 8.G.6 Standards moved from 7th grade

14 More on the Angles of a Triangle 8.G.5 8.G.5 None15 Informal Proof of the Pythagorean Theorem (Optional) 8.G.6 & 8.G.7 8.G.7 & 8.G.8 None16 Applications of the Pythagorean Theorem (Optional) 8.G.6 & 8.G.7 8.G.7 & 8.G.8 None

5 EXAMPLES OF FUNCTIONS FROM GEOMETRY1 Concept of a Function 8.F.1, 8.F.2, 8.F.3 8.F.1, 8.F.2, 8.F.3 8.F.1 &2 (Wording) 3 (None)2 Formal Definition of a Function 8.F.1, 8.F.2, 8.F.3 8.F.1, 8.F.2, 8.F.3 8.F.1 &2 (Wording) 3 (None)3 Linear Functions and Proportionality 8.F.1, 8.F.2, 8.F.3 8.F.1, 8.F.2, 8.F.3 8.F.1 &2 (Wording) 3 (None)4 More Examples of Functions 8.F.1, 8.F.2, 8.F.3 8.F.1, 8.F.2, 8.F.3 8.F.1 &2 (Wording) 3 (None)5 Graphs of Functions and Equations 8.F.1, 8.F.2, 8.F.3 8.F.1, 8.F.2, 8.F.3 8.F.1 &2 (Wording) 3 (None)6 Graphs of Linear Functions and Rate of Change 8.F.1, 8.F.2, 8.F.3 8.F.1, 8.F.2, 8.F.3 8.F.1 &2 (Wording) 3 (None)7 Comparing Linear Functions and Graphs 8.F.1, 8.F.2, 8.F.3 8.F.1, 8.F.2, 8.F.3 8.F.1 &2 (Wording) 3 (None)8 Graphs of Simple Non-Linear Fucntions 8.F.1, 8.F.2, 8.F.3 8.F.1, 8.F.2, 8.F.3 8.F.1 &2 (Wording) 3 (None)9 Examples of Functions from Geometry 8.G.9 8.G.10 & 12 8.G.12 New standard in 2017

Assess Mid Module AssessmentNEW STANDARD Investigating relationships of 3-D figures (3 lessons) n/a 8.G.11 New standard in 2017

USD #457 8th Grade Eureka Specific Pacing Suggestions

NEW Surface Area of Pyramid and Cone (3 lessons) G.GMD.3 8.G.11b Standard moved from HSNEW Volume of a Pyramid (3 lessons) G.GMD.3 8.G.11a Standard moved from HS

10 Volumes of Familiars Solids- Cones and Cylinders 8.G.9 8.G.10 & 12 8.G.12 New standard in 201711 Volume of a Sphere 8.G.9 8.G.10 & 12 8.G.12 New standard in 2017

Assess End Module Assessment6 LINEAR FUNCTIONS

1 Modeling Linear Relationships 8.F.4 & 8.F.5 8.F.4 & 8.F.5 None2 Interpreting Rate of Change and Initial Value 8.F.4 & 8.F.5 8.F.4 & 8.F.5 None3 Representations of a Line 8.F.4 & 8.F.5 8.F.4 & 8.F.5 None4 Increasing and Decreasing Functions 8.F.4 & 8.F.5 8.F.4 & 8.F.5 None5 Increasing and Decreasing Functions 8.F.4 & 8.F.5 8.F.4 & 8.F.5 None6 Scatter Plots 8.SP.1 & 8.SP.2 8.SP.1 & 8.SP.2 None7 Patterns in Scatter Plots 8.SP.1 & 8.SP.2 8.SP.1 & 8.SP.2 None8 Informally Fitting a Line 8.SP.1 & 8.SP.2 8.SP.1 & 8.SP.2 None9 Determining the Equation of a line Fit to Data 8.SP.1 & 8.SP.2 8.SP.1 & 8.SP.2 None

10 Linear Models 8.SP.1, 8.SP.2, 8.SP.3 8.SP.1, 8.SP.2, 8.SP.3 None11 Using Linear Models in a Data Context 8.SP.1, 8.SP.2, 8.SP.3 8.SP.1, 8.SP.2, 8.SP.3 None12 Non-Linear Models in a Data Context (Optional) 8.SP.1, 8.SP.2, 8.SP.3 8.SP.1, 8.SP.2, 8.SP.3 None

Assess End Module Assessment7 Part 1 INTRO TO IRRATIONAL NUMBERS USING GEOMETRY

2 Square Roots 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)3 Exsistence and Uniqueness of Square Roots and Cubed Roots 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)4 Simplifying Square Roots (Optional) 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)5 Solving Equations with Radicals 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)6 Finite and Infinite Decimals 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)7 Infinite Decimals 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)

3 SIMILARITYAdd lessons to addres 8.G.5 (3 lessons) 8.G.5 8.G.5

13 Proof of Pythagorean Theorem 8.G.6 & 8.G.7 8.G.7 & 8.G.8 None14 Converse of Pythagorean Theorem 8.G.6 & 8.G.7 8.G.7 & 8.G.8 None

Assess End-Module Assessment1 INTEGER EXPONENTS AND SCIENTIFIC NOTATION

7 Magnitude 8.EE.3 & 8.EE.4 8.EE.2 & 3 None8 Estimating Quantities 8.EE.3 & 8.EE.4 8.EE.2 & 3 Wording on 8.EE.49 Scientific Notation 8.EE.3 & 8.EE.4 8.EE.2 & 3 Wording on 8.EE.4

10 Operations with Numbers in Scientific Notation 8.EE.3 & 8.EE.4 8.EE.2 & 3 Wording on 8.EE.411 Efficacy of Scientific Notation 8.EE.3 & 8.EE.4 8.EE.2 & 3 Wording on 8.EE.413 Comparison of Numbers written in Scientific Notation and Interpreting Scientific Notation Using Technology 8.EE.3 & 8.EE.4 8.EE.2 & 3 Wording on 8.EE.4

Assess End-Module Assessment7 Part 2 INTRO TO IRRATIONAL NUMBERS USING GEOMETRY

8 Long Division Algorithm 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)9 Decimal Expansions of Fractions Pt.1 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)

10 Converting Repeating Decimals to Fractions 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)11 Decimal Expansion of some Irrational Numbers 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)12 Decimal Expansions of Fractions Pt.2 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)13 Comparing Irrational Numbers 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)14 Decimal Expansion of Pi 8.NS.1, 8.NS.2, 8.EE.2 8.EE.1 8.EE.1 (wording)

Assess Mid-Module Assessment15 Pythagorean theorem Revisted 8.G.6, 8.G.7, 8.G.8 8.G.7, 8.G.8, 8.G.9 None16 Converse of the Pythagorean Theorem 8.G.6, 8.G.7, 8.G.8 8.G.7, 8.G.8, 8.G.9 None17 Distance on the Coordinate Plane 8.G.6, 8.G.7, 8.G.8 8.G.7, 8.G.8, 8.G.9 None18 Applications of the Pythagorean Theorem 8.G.6, 8.G.7, 8.G.8 8.G.7, 8.G.8, 8.G.9 None19 Cones and Spheres 8.G.7, 8.G.9 8.G.8, 8.G.10 &12 8.G.12 (New)20 Truncated Cones 8.G.7, 8.G.9 8.G.8, 8.G.10 &12 8.G.12 (New)21 Volume of Composite Solids 8.G.7, 8.G.9 8.G.8, 8.G.10 &12 8.G.12 (New)22 Average Rate of Change 8.G.7, 8.G.9 8.G.8, 8.G.10 &12 8.G.12 (New)23 Non Linear Motion 8.G.7, 8.G.9 8.G.8, 8.G.10 &12 8.G.12 (New)

Assess End Module Assessment8 GRAPHING CALCULATORS (Garden City Addition)

Section 8 is additional curriculum to help students become acquainted with the basic functions of a graphing calculator as it will be needed within the first unit in Algebra 1 at the high school. A graphing calculator app is available for the iPads free of charge.

Problem Solving Tasks

During each module you teach, students will participate in 2 days of

problem solving tasks. It is at the discretion of the classroom teacher as to when the 2 days of problem solving will take place during each module, as well as which problem solving tasks will be completed. A list of suggested curriculum-aligned resources can also be found within the USD#457 K-12 Mathematics Framework. Direct digital links to the resources listed can also be found at www.gckschools.com/candi/math.

Additional problem solving tasks can be used if they are identified as being

high quality mathematical tasks. An Identifying High-Quality Tasks or Supplemental Resources tool can be found within the USD #457 K-12 Math Mathematics Framework. The tool identifies characteristics that are consistently found in high quality tasks.